The Union of Supernova (you can get the dataset from heresupernova datasetsupernova datasetIa that were used to declare that the expansion of the universe is expanding is explained very simply by a static Einstein universe. The raw dataset comes with redshift and distance modulus , so the distance is . The plot of distance versus redshift looks like this graphic:

The x-axis is distance in parsecs and the y-axis is where is the frequency of the H-alpha line.

The adjustment is made as follows, we assume a universe of radius and consider the adjusted redshift where . This is not necessarily the optimal choice theoretically but it is a rough translation of the comparison of eigenfunctions of Laplacian on a circle of radius as to the eigenfunctions of the Laplacian on a three-sphere as . Then I chose to minimize variance of the corrected redshifts. The variance of redshifted wavelengths in the dataset (in meters) is while this procedure leads to which is not fundamental. What is important is that the variance of the corrected redshift is . The variance reduction for the (observed redshifted wavelengths) is 0.9826, and the resulting distance/corrected redshift graph is the following:

This graph for supernova dataset would not be indicative of any accelerated expansion of the universe. The important point in this exercise is that the correction to the observed redshift is done with an extremely simple assumption that the ‘cosmological redshift’ is due ONLY to the static spherical geometry of spatial section say in a comoving frame which is the static Einstein spacetime with a fixed radius. The explanation that I have for the redshift is NOT tired light. It is simply that if space is curved then the waves on the space will not have the usual wavelength-distance relation and therefore we would expect a redshift that is not a physical phenomenon of interest beyond curvature. Photons are assumed to follow the classical Maxwell’s equation which can be modified with a quantum field theoretic model etc. etc. But the main issue is that redshift is a purely geometric phenomenon and not due to any special interactions that photons experience all classical waves will have this feature. So there is no expansion of the universe that need be explained by the redshift and no accelerated expansion on supernova data. There need be no dark energy either.

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